How to make a somewhat stiff pneumatic tube?
You can use a cloth simulation for this.

Scene Setup
To begin with, I added a simple bezier curve, then edited and beveled it. I then converted it to a mesh object, and built the other simple cuboid mesh object you can see in the pictures.
Next, go into edit mode on the curve (now a mesh), and select the ending vertices to setup a vertex group to pin them. Add a new vertex group and assign these verts to it.

Parent the curve to the cuboid mesh (that means the curve mesh becomes the child of the other), and add a cloth simulation in the physics tab of the properties panel.
Note: All of the above should be trivial, but if you need more information, let me know.
Cloth Simulation Setup

I disabled everything in the cloth settings except for pinned vertex group.



I started with the &quot;leather&quot; preset, as I felt that was closest to the desired physics settings.

The quality steps is not super important to keep high, but will be noticeable if set low (e.g., below 5).

If the speed multiplier is set lower, things look more like string (they move faster); if set high, it looks more like the desired tubing (I used a value of 3 in the demo).

Make sure to setup the vertex group for pinned verts by enabling &quot;pinning&quot; and then setup a vertex group (assign the vertices that are on the edges of the tube) for it.

I decreased the &quot;bending&quot; relative to the leather preset. As the tooltip says, it basically sets the size of the waves: higher is bigger, lower is smaller.

I increased the &quot;structural&quot; stiffness factor because the tubing has a more stiff overall stiffness than leather would.

I decreased the &quot;spring&quot; damping from 25 to 15, because I wanted a bit more jiggling when I did the shake animation.

I increased the &quot;air&quot; damping to slow it down further. This seems to behave similarly to the &quot;multiplier&quot; setting, although the values are entirely different.